Given: X and Y, independent, continuous

**uniform** random variables on the interval (0,1)

Goal: Find the density function of

My approach:

Use the transformation technique (as in point 5 of this wikipedia page

Integration by substitution - Wikipedia, the free encyclopedia).

Define

. Define

.

I find that the joint density of

and

is

And this is where i get stuck... I tried integrating

out of it but nothing reasonable comes out (not a density function anyway). So two questions:

- Did I find the joint density correct?
- I tried integrating over the interval to 1, is this correct?
- What should be next step?

Thanks for any help!